When a player draws their last card do they refresh?

No, drawing the last card in your deck does not cause you to "refresh" or recycle your trash.

In Riftbound, you only perform a "Burn Out" (which includes recycling your trash into your Main Deck) if you are instructed to draw a card and your Main Deck is empty.

According to Rule 413.4 and Rule 431.1:

• Drawing the last card: As long as there is at least one card in your deck, you simply draw it normally. Your deck is now empty, but no penalty or action is triggered.
• Attempting to draw from an empty deck: If you are instructed to draw a card while your deck is already empty, you trigger a Burn Out. Per Rule 431.2, you must then:
  1. Recycle your trash into your Main Deck (randomizing it).
  2. Choose an opponent to gain 1 point.
  3. Complete the original draw instruction.